2. Section 9-6 Solving Rational Equations and Inequalities Ryann Noe

3. Rational equation: Rational Inequalities: any equation that contains one or more rational expressions Ex: Inequalities that contain one or more rational expressions Ex:

4. Solving Rational Equations Easier to solve once fractions are eliminated Eliminate by using Least Common Denominator FRACTIONS

5. Multiply out 33-4=x x=29 Answer!

6. Find LCD then SolveCheck your solution LCD= 28(z+2) multiply (9z+18) + 84 = 21z + 42 9z + 102 = 21z + 42 60 = 12z 5 = z

7. CHECK True so: Z=5

8. Solving Inequalities Excluded values: 1.State the excluded values 2.Change the sign to equals and solve 3.Use the values found by solving to make a number line and then test points values that make the denominator equal to zero

9. example: 1.The only excluded value is 0 2.Solve: 2+5=4a 7=4a a=

10. On your number line draw vertical lines at the excluded number and your solution to separate into regions -3-20123 Then test a value in each section and see which number comes out true

11. Test a= –1 This is NOT true so a<0 is not a solution

12. Test a=1 True so: 0<a<

13. Test a=2 This is NOT true so a> is not a solution This means that the final answer is 0<a<

14. Homework Page 510 # 11-37 odd